The Aspen Art Museum is getting ready to attempt the art-world equivalent of a double black diamond.

After three decades of shoehorning contemporary-art exhibits into a former power plant on the outskirts of this wealthy Rocky Mountain enclave, the museum plans to triple its footprint. It will relocate in August to a new home designed by Pritzker prize winner Shigeru Ban in the center of town—a move that illustrates the growing clout and ambition of Aspen's stewards.

Mr. Ban, who is known for using unconventional materials like paper and cardboard tubes, has created a three-story building that resembles an enormous wooden crate. The 33,000-square-foot facility, which opens Aug. 9, has walls of wood veneer planks woven into latticework. The grid covers a glass wall, giving passersby a glimpse inside.

The building has a rooftop sculpture garden with a panoramic view of Ajax Mountain, said director Heidi Zuckerman Jacobson.

The $72 million project caps a near-decade-long campaign by Ms. Zuckerman Jacobson to elevate the Aspen Art Museum from a local showcase for traveling exhibits of crafts and Western memorabilia to a can't-miss stop on the contemporary-art circuit. To pull it off, the museum had to rally Aspen's coterie of seasonal residents who also happen to rank among the world's top art buyers. They include former Gucci Group Chief Executive Domenico De Sole and John Phelan, co-founder of investment firm MSD Capital, LP. The board is now stocked with contemporary-art powerhouses, who share Ms. Zuckerman Jacobson's vision of an institution with the curatorial sweep of New York's Museum of Modern Art, a number of trustees said. (The project's tab includes a $27 million endowment.)

Ms. Zuckerman Jacobson developed her art-world contacts through her career as a curator. Before Aspen, she worked at the University of California's Berkeley Art Museum and the Jewish Museum in New York.

Dallas collector Gayle Stoffel, who has been coming to Aspen for 25 years with her husband, Paul, to ski, said she used to skip the museum altogether. That changed eight years ago, when Ms. Zuckerman Jacobson arrived and shifted the focus to living artists and unusual collaborations. Ms. Stoffel now is co-chairman of the museum's national council.

The museum also retooled its programs to play up the flexibility it gets from styling itself as a kunsthalle, a German term for a noncollecting museum. That distinguishes Aspen, which focuses on commissioning works by artists, from museums that concentrate on building a collection.

Although kunsthalles are common in Europe, there are only about a half-dozen in the U.S., according to the American Alliance of Museums. It means that the Aspen Art Museum can direct much of its budget to putting on exhibits instead of storing or conserving a permanent collection. Right now, roughly 70% of the art Aspen exhibits is new, commissioned directly from artists by the museum. Artists often are invited to create on site or nearby; in many cases, the commissioned works return to the artist after a show.

On Aug. 2, firework artist Cai Guo-Qiang plans to unveil "Black Lightning," a lightning-bolt-shape firework he will set off from the top of Ajax Mountain. Jim Hodges, who creates delicate, metal spiderweb sculptures, will cover a portion of the museum's exterior in 6-foot-high mirrored letters that repeat the phrase "with liberty and justice for all" from the Pledge of Allegiance. The words are fitting, Ms. Zuckerman Jacobson said, because the museum's new location is near Independence Pass, a historic route for settlers heading West.

Inside, there will be a show of 50 works by Yves Klein and David Hammons, iconoclastic artists known for burning and mangling their canvases.

Ms. Zuckerman Jacobson said "showing the unexpected" was the only way to attract more attention, especially in the museum's original, out-of-the-way location. Ultimately, she said she hopes to double the current 40,000 annual visitors.

That is a tall order for a town with a year-round population of 6,600. Brad Smith, managing partner of a nearby restaurant called the Red Onion, said some locals joke that the new museum's woven slats make it resemble a prison more than a crate. But most residents are cautiously optimistic about the building, he said. "Some people feel like it's a monster because it's so big," Mr. Smith added. "But I've got young children, so I'll go."

Corrections & Amplifications

The Aspen Art Museum director is Heidi Zuckerman Jacobson. An earlier version of this story incorrectly identified her on second reference as Ms. Jacobson and not Ms. Zuckerman Jacobson. Also, the new museum is near Independence Pass, not atop it, as the story initially said.

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